# How do you factor #5x^4 + x^3 - 22x^2 - 4x + 8#?

##### 1 Answer

The result is

The procedure is the following:

You have to apply Ruffini's Rule trying the divisors of the independent term (in this case, the divisors of 8) until you find one that makes the rest of the division zero.

I started with +1 and -1 but it did not work, but if you try (-2) you get it:

```
! 5 1 -22 -4 8
-2! -10 +18 +8 -8
_____________________
5 -9 -4 +4 0
```

What you have here is that

Now you have got one factor (x+2) and you have to keep going the same process with

If you try now with +2 you will get it:

```
! 5 -9 -4 4
2 ! 10 2 -4
__________________
5 +1 -2 0
```

So, what you have now is that

And summing up what we have done until now:

Now, you have got two factors: (x+2) and (x-2) and you have to decompose

In this case, instead of applying Ruffini's Rule, we shall apply the classic resolution formula to the quadratic equation:

So what we have now is that

So the solution is: